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Chvátal-Erdos condition and pancyclism

100%

Flandrin E., Li H., Marczyk A., Schiermeyer I., Woźniak M.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 2

335-342

The well-known Chvátal-Erdős theorem states that if the stability number α of a graph G is not greater than its connectivity then G is hamiltonian. In 1974 Erdős showed that if, additionally, the order of the graph is sufficiently large with respect to α, then G is pancyclic. His proof is based on the properties of cycle-complete graph Ramsey numbers. In this paper we show that a similar result can be easily proved by applying only classical Ramsey numbers.

Extending the MAX Algorithm for Maximum Independent Set

72%

Lê N. C., Brause C., Schiermeyer I.

Discussiones Mathematicae Graph Theory

2015

tom 35

nr 2

365-386

The maximum independent set problem is an NP-hard problem. In this paper, we consider Algorithm MAX, which is a polynomial time algorithm for finding a maximal independent set in a graph G. We present a set of forbidden induced subgraphs such that Algorithm MAX always results in finding a maximum independent set of G. We also describe two modifications of Algorithm MAX and sets of forbidden induced subgraphs for the new algorithms.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Schiermeyer I.

1 Brause C.

1 Flandrin E.

1 Li H.

1 Lê N. C.

1 Marczyk A.

1 Woźniak M.

1 2015

1 2006

Wyniki wyszukiwania

Chvátal-Erdos condition and pancyclism

Extending the MAX Algorithm for Maximum Independent Set